Question

Determine the shaded area.The shaded area is(Type an integer or decimal rounded to the nearest hundredth

Answer 1

The shaded area is equal to the area of the circle substracted fromt he area of the trapezoid:

$A=A_T-A_C$

Area of a trapezoid:

$A_T=\frac{(a+b)}{2}\cdot h$

a is long base

b is short base

h is height

Area of a circle:

$A_C=\pi\cdot r^2$

The given trapezoid has a height equal to 2 times the radius of the circle in it. Then, the area of the shaded area is:

$A=\frac{(a+b)}{2}\cdot2r-\pi\cdot r^2$

a=13in

b=9in

r=3in

$\begin{gathered} A=\frac{(13in+9in)}{2}\cdot2(3in)-\pi\cdot(3in)^2 \\ \\ A=\frac{(22in)}{2}\cdot6in-9\pi in^2 \\ \\ A=66in^2-9\pi in^2 \\ \\ A\approx37.73in^2 \end{gathered}$